A fast and automatic identification method for structural surfaces based on high-precision point cloud data

Abstract

This invention discloses a method for rapid and automatic identification of structural surfaces based on high-precision point cloud data. To address the problem of slow regional growth and significant influence of the threshold of the growth criterion when segmenting structural surfaces, the concept of fuzzy boundaries is introduced to reduce the impact of the threshold on regional growth. Simultaneously, a pre-allocated search space accelerates the segmentation of regional growth, resulting in a rapid and accurate method for segmenting structural surfaces. While ensuring accurate identification of structural surfaces, this method rapidly extracts geological information about structural surfaces and improves the efficiency of obtaining this information through an automated algorithm.

Description

Technical Field

[0001] The present invention belongs to the field of surveying and mapping engineering, and in particular relates to a method for rapid and automatic identification of structural surfaces based on high-precision point cloud data. Background Art

[0002] 3D laser scanning, a non-contact measurement technology, boasts fast data acquisition, high accuracy, full automation, and all-weather operation. It has become a crucial technology for acquiring geospatial data. To interpret the geographic information contained in massive amounts of 3D spatial data, clustering and segmenting the data into manageable subcategories is the primary method.

[0003] Cluster analysis is an unsupervised classification method that groups datasets without requiring or requiring minimal prior knowledge. However, geographic information, especially structural surface information, often has boundaries based on engineering experience and is therefore fuzzy. Fuzzy clustering, however, describes element similarities probabilistically, thus better aligning with practical engineering and empirical knowledge. Furthermore, fuzzy clustering is flexible and less susceptible to noise, leading to its widespread application.

[0004] Region growing is a segmentation algorithm with the advantages of simple principle, easy implementation, and detailed segmentation. However, the following problems remain: ① Traditional region growing methods consider all elements in a dataset as possible growth targets, requiring each element to be determined for its growth possibility. This aims to ensure algorithm accuracy, but when the dataset is too large and most elements are not possible growth elements, the algorithm spends a significant amount of time processing unnecessary data, resulting in slow growth and wasted runtime and storage space. ② Furthermore, traditional region growing criteria use fixed thresholds, requiring absolute separation of regions to ensure accurate results. Such criteria are difficult to find, and fixed criteria result in distinct regions, making them unsuitable for segmenting structural surfaces with relatively fuzzy boundaries.

[0005] Many achievements have been made in the field of structural surface recognition: Gigli and Casagli performed spatial voxel segmentation on point clouds, designed a semi-automatic structural surface recognition method, and summarized the extraction methods of structural surface geological information; (Gigli and Casagli, Semi-automatic extraction of rock mass structural data from high-resolution LIDAR point clouds [J]. International Journal of Rock Mechanics and Mining Sciences. 2011 (48), 187-198.) Riquelme used the k-means (k-means clustering) method to realize the automatic recognition method of structural surface. (Riquelme et al., Identification of Rock Slope Discontinuity Sets from Laser Scanner and Photogrammetric Point Clouds: A Comparative Analysis [J]. Procedia Engineering. 2017 (191), 838-845.). In addition, Dong Xiujun also realized the automatic recognition of structural surfaces by coloring the point cloud in HSV color space and clustering. (A method for identifying and extracting rock mass structural surfaces based on 3D laser scanning [P]. Dong Xiujun, et al. Chinese Patent: CN112529844A, 2021-03-19.)

[0006] However, point cloud data is becoming increasingly large and complex, and many projects require timely acquisition of structural surface information. This places higher demands on the rapid and accurate acquisition of structural surface geological information. Preliminary research on the acquisition of structural surface geological information has been conducted both domestically and internationally, but the accuracy and speed of structural surface geological information extraction need to be further improved. Summary of the Invention

[0007] To address the technical problems encountered in the prior art, this invention provides a method for rapid and automatic identification of structural surfaces based on high-precision point cloud data. This novel method utilizes fuzzy clustering to generate a three-dimensional model of structural surfaces, optimizing region growing to achieve rapid segmentation of structural surfaces. While ensuring segmentation accuracy, this method effectively improves the accuracy of structural surface identification and can complete structural surface identification on point clouds containing millions of data points in just minutes, thereby increasing the efficiency of geological surveying.

[0008] In order to solve the technical problem, the technical solution of the present invention is:

[0009] A method for rapid and automatic identification of structural surfaces based on high-precision point cloud data, the method comprising:

[0010] After setting the triangle size of the triangulated network model to match the pre-processed point cloud data, the triangulated network model is established using the triangulation algorithm;

[0011] Calculate the normal vector of the triangulated mesh based on the triangulated mesh model, and normalize the normal vector of the triangulated mesh to the unit sphere space to obtain the normalized result of the triangulated mesh normal vector;

[0012] Sort all triangles in the triangulated network model to obtain the sorting result;

[0013] Based on the normalization result of the triangulated network normal vector, the initial cluster center V is estimated, and the fuzzy clustering is iteratively completed to obtain the fuzzy clustering result;

[0014] Based on the sorting results and fuzzy clustering results, the predicted growth objects are pre-screened and the regional growth seeds are replaced until the structural surface segmentation is completed and the separation results of all structural surfaces are obtained.

[0015] Furthermore, before processing the pre-processed point cloud data, the method further includes:

[0016] By arranging multiple stations, the measurement area is scanned with high precision from multiple angles to obtain high-precision point cloud data from multiple stations.

[0017] Furthermore, the high-precision point cloud data of multiple sites are stitched and denoised to obtain preprocessed point cloud data.

[0018] Furthermore, based on the preset value of the structural surface recognition accuracy, the triangle size of the corresponding triangulated network model is set, and then the triangulated network model is established using the Delaunay triangulation algorithm. The N triangular facets of the model are stored in the form of triangle vertices and vertex indices; the triangle vertices are the coordinates (x, y, z) of the point cloud, which is the same as the number of points in the point cloud; the vertex index is (a i , b i , c i )The three vertices are arranged in a clockwise direction.

[0019] Furthermore, the calculation of the normal vector of the triangulated network specifically includes:

[0020] According to the triangle vertex and vertex index, the vertex index is traversed and calculated as i(a i , b i , c i )'s triangle's external normal vector F i , and normalize it to the unit sphere space; the calculation method is as follows:

[0021]

[0022]

[0023]

[0024] Furthermore, all triangles in the triangulated network model are sorted, including:

[0025] Sort all triangles in the triangulated network based on the distance R from the triangle center to the origin. If multiple triangles are located in the same sphere, sort them by elevation. After the sorting is completed, adjacent triangles are within a spherical shell of a certain thickness, that is:

[0026]

[0027] sort(R)→R1≤R2…≤R n .

[0028] Furthermore, the estimating of the initial cluster center V and iteratively completing the fuzzy clustering specifically includes:

[0029] If the initial cluster center and the number of clusters K are set, and the cosine distance is used to calculate the dissimilarity index d of the spherical space data, then the dissimilarity d of the i-th triangle relative to the j-th center is ij for:

[0030] d ij 2 =1-(F i ·V j ) 2 , F i ●V j is the vector F i With V j The vector product of

[0031] Calculate the membership function matrix U of fuzzy clustering. For any triangle face i, its membership degree u to the jth cluster center is ij for:

[0032]

[0033] If the number of clusters is not set, the traversal will start from 2; m is the fuzziness. When m=2, it can meet most clustering requirements. It is the default value of the program and can be changed according to the actual situation.

[0034] If the initial cluster center and the number of clusters K are not set, a random algorithm will be used to generate the membership function matrix U, and then the cluster center V will be calculated; the calculation of the j-th cluster center is:

[0035]

[0036] Then calculate the membership function matrix U under this cluster center;

[0037] The new cluster center V* is calculated by the membership function matrix U calculated above, and the new membership function matrix U* is calculated by the new cluster center V* until the objective function J of the fuzzy clustering is obtained. m When the (U, V) function is at its minimum, clustering is complete; the objective function J of fuzzy clustering is m The calculation of the (U,V) function is:

[0038]

[0039] When the membership function matrix objective function J of the two iterations m , J m * When it is less than the set allowable error ε, the algorithm is judged to have converged, and the discriminant of the algorithm termination iteration is:

[0040] J m -J m * <ε,ε=10 -5 .

[0041] Furthermore, the pre-screening of the predicted growth objects specifically includes:

[0042] When the growing seed is located within a small sphere (R d1 ), then the predicted growth object is within the large sphere (R d2 ) and the spherical shell area outside the small sphere; the thickness of the spherical shell is determined by the maximum triangle size d max It was decided that in order to ensure that all predicted growth objects are located in this area, 5 times the maximum triangle size is taken as the pre-screened spherical shell thickness R0;

[0043] Right now:

[0044] R0=5*max(d);

[0045] R d2 =R d1 +R0.

[0046] Furthermore, the replacing of the regional growth seeds until the structural surface segmentation is completed specifically includes:

[0047] I: Select a triangle as the growth seed;

[0048] Ii: Search for a triangle in the spherical shell that shares a common edge with the seed triangle. This triangle is the triangle that may be needed for growth.

[0049] III: Define the growth principle, and only perform region growing when the triangles with the same edge and the seed triangle have fuzzy clustering results;

[0050] IV: Repeat steps i-iii above using the growing triangle as a seed triangle until the growth stops (no triangles with common edges that match the fuzzy clustering results are found in the spherical shell), completing the separation of a structural surface.

[0051] V: Replace the new growth seed and repeat the above steps i-iv until all triangles are separated. At this time, all structural surfaces are separated.

[0052] Furthermore, after obtaining the separation results of all structural surfaces, the method further includes:

[0053] Calculate geological information of each structural surface:

[0054] I: Occurrence information: The normal vector n(x, y, z) of the structural surface is the average value of the normal vector of its triangle surface. The corresponding relationship between the normal vector n and the inclination angle θ should be classified according to the different hexagons in which the normal vector n is located, as follows:

[0055]

[0056] ii: Structural surface exposed area: The structural surface exposed area is the sum of the areas of all triangular facets belonging to it.

[0057] III: Structural surface trace length: The maximum length of the structural surface along the dip or strike direction is taken as the trace length, that is, the triangle exposed on the structural surface is projected along the dip or strike direction, and the maximum value of the projection length is taken as the trace length.

[0058] Compared with the prior art, the advantages of the present invention are:

[0059] This invention addresses the problem of slow regional growth and significant influence of the growth criterion threshold when segmenting structural surfaces. By introducing the concept of fuzzy boundaries, this approach reduces the impact of the threshold on regional growth. Furthermore, by pre-allocating the search space, this method accelerates regional growth segmentation and proposes a fast and accurate method for segmenting structural surfaces. While ensuring accurate identification of structural surfaces, this method rapidly extracts geological information about the structural surfaces and employs an automated algorithm to improve the efficiency of obtaining this information. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 , fuzzy clustering diagram;

[0061] Figure 2 : Schematic diagram of region growing;

[0062] Figure 3 : Schematic diagram of structural surface measurement;

[0063] Figure 4 : Select measurement area map;

[0064] Figure 5 : Calculation diagram of triangulated external normal vector;

[0065] Figure 6 : Structural surface recognition result diagram. DETAILED DESCRIPTION

[0066] The specific implementation of the present invention is described below in conjunction with examples:

[0067] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the efficacy and purpose that can be achieved by the present invention.

[0068] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" quoted in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0069] Example 1

[0070] (1) High-precision point cloud acquisition. Arrange multiple stations to perform high-precision scanning of the measurement area from multiple angles, and perform encrypted scanning to meet accuracy requirements.

[0071] (2) Point cloud stitching and noise reduction. The data from multiple sites are stitched together, and noise points caused by external interference such as instrument vibration, dust, etc., as well as unnecessary areas are deleted.

[0072] (3) Generate triangulated mesh model. Import point cloud data, set the corresponding triangulated mesh model triangle size according to the accuracy requirements of structural surface recognition, and then use the Delaunay triangulation algorithm to build the triangulated mesh model. The N triangular facets of the model are represented by triangle vertices (the coordinates of the point cloud, (x, y, z), the same as the number of points in the point cloud) and vertex index ((a i , b i , c i )The three vertices are stored in a clockwise order.

[0073] (4) Calculate the normal vector of the triangulated network. According to the triangle vertex (the coordinates of the point cloud) and the vertex index, calculate the external normal vector F of the triangle face i i, and normalize it to the unit sphere space. The calculation method is as follows:

[0074]

[0075]

[0076]

[0077] (5) Sort the triangulated network model. Sort all triangles in the triangulated network by the distance R from the center of the triangle to the origin. If multiple triangles are located in the same sphere, sort them by elevation. After sorting, adjacent triangles are always within a spherical shell of a certain thickness. See the attached diagram for details. Figure 1 .Right now:

[0078]

[0079] sort(R)→R1≤R2…≤R n

[0080] (6) Set the initial cluster center V and the number of clusters K. If the number of structural surface groups and dominant directions in the survey area can be obtained based on relevant data or previous geological surveys, setting the initial cluster center and the number of clusters based on prior knowledge can improve the accuracy of structural surface identification. If there is no relevant data, proceed to the next step.

[0081] (7) Estimate the initial cluster center V and iterate to complete the fuzzy clustering (such as Figure 1 The process is as follows:

[0082] If the initial cluster center is set, the cosine distance is used to calculate the dissimilarity index d of the spherical space data, then the dissimilarity d of the i-th triangle relative to the j-th center is ij for:

[0083] d ij 2 =1-(F i ·V j ) 2 , F i ●V j is the vector F i With V j The vector product of

[0084] Then calculate the membership function matrix U of fuzzy clustering. For any triangle face i, its membership degree u to the jth cluster center is ij for:

[0085]

[0086] If the number of clusters is not set, the traversal will start from 2; when m is the fuzziness, m=2 can meet most clustering requirements and is the default value of the program.

[0087] ii. If the initial cluster center is not set, a random algorithm will be used to generate the membership function matrix U, and then the cluster center V will be calculated. The calculation of the jth cluster center is:

[0088]

[0089] Then calculate the membership function matrix U under this cluster center.

[0090] iii. Calculate the new cluster center V* through the membership function matrix U calculated last time, and calculate the new membership function matrix U* through the new cluster center V*. Until the objective function J of fuzzy clustering is m When the (U, V) function reaches its minimum value, clustering is completed. The objective function J of fuzzy clustering is m The calculation of the (U,V) function is:

[0091]

[0092] But in order to prevent excessive iteration, when the membership function matrix objective function J of two iterations m , J m * When it is less than the set tolerance ε, the algorithm is considered to have converged. The discriminant of the algorithm termination iteration is:

[0093] J m -J m * <ε,ε=10 -5 .

[0094] (9) Pre-screening of possible growth objects. When the growth seed is located on a small spherical surface (on) R d1 , then the possible growth object is the inner (upper) R d2 And the spherical shell area outside the small ball surface is attached Figure 2 The thickness of the spherical shell is determined by the maximum triangle size d of the triangulated network. max It is decided that in order to ensure that all possible growth objects are located in this area, 5 times the maximum triangle size is taken as the pre-screened spherical shell thickness R0. That is:

[0095] R0=5*max(d);

[0096] R d2 =R d1 +R0;

[0097] (10) Replace the regional growth seed until the structural surface segmentation is completed (such as Figure 2 The complete steps are as follows:

[0098] i get{R d1}, {growth}+={R d1};

[0099] Select a triangle as the growth seed;

[0100] ii R d2 =Rd1+R0, {growth0}=(R d1 :R d2 )∩R d1 ;

[0101] Search for a triangle in the spherical shell that shares a common edge with the seed triangle. This triangle is the triangle that may be needed for growth.

[0102] iii{growth}+=(Id{growth0}==Id(R d1 ));

[0103] Define the growth principle, and only perform region growing when the triangles with the same edge and the seed triangle have fuzzy clustering results;

[0104] iv{R d1}={growth}, go loop(i:iii), end, cluster={growth}, delete R{growth};

[0105] The growing triangle is used as a seed triangle and the above steps are repeated until the growth stops (no triangle with a common edge of the fuzzy clustering result is found in the spherical shell), completing the separation of a structural surface;

[0106] v go loop(i:iv), end;

[0107] Replace new growth seeds until all triangles are separated, at which point all structural faces are separated.

[0108] (11) Calculate the orientation of each structural surface. The normal vector n(x, y, z) of the structural surface is the average value of the normal vectors of its triangles. The corresponding relationship with the inclination angle θ should be discussed according to the different categories of the hexagons where the normal vector n is located. The details are as follows:

[0109]

[0110] (12) Structural surface exposed area and trace length (such as Figure 3The exposed area of ​​the structural surface is the sum of the areas of all triangular facets belonging to it. The maximum length of the structural surface along the dip or strike direction is taken as the trace length. That is, the triangle exposed on the structural surface is projected along the dip or strike direction, and the maximum value of the projection length is taken as the trace length.

[0111] (13) Output structural surface information.

[0112] Example 2:

[0113] The specific implementation of this method is described below with reference to specific examples.

[0114] (1) Conduct on-site surveys, perform relevant field work, and keep relevant records; obtain point clouds of the measurement area;

[0115] (2) After completing the point cloud stitching and noise reduction, select the area to be measured (see Appendix Figure 4 );

[0116] (3) According to the results of the field investigation and the measurement accuracy requirements, the triangle size of the triangulated network model is set, and the triangulated network model is generated and optimized (see Appendix Figure 5 );

[0117] (4) Calculate the normal vector outside the triangulation network (see Appendix Figure 5 );

[0118] (5) The algorithm automatically performs fuzzy clustering and region growing to complete structural surface identification. The clustering results are shown in the attached Figure 6 ;

[0119] (6) Measure structural surface information;

[0120] (7) Output structural surface measurement data.

[0121] In this embodiment, the algorithm processes about 780,000 triangulated network data on a computer with an i5-10400F CPU and 8GB RAM, and it takes a total of 5 minutes.

[0122] Appendix: Partial structural surface information table

[0123]

[0124]

[0125] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0126] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0127] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0128] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the scope of the present invention.

[0129] Many other changes and modifications can be made without departing from the spirit and scope of the present invention. It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for rapid and automatic identification of structural surfaces based on high-precision point cloud data, characterized in that: The method comprises: After setting the triangle size of the triangulated network model to match the pre-processed point cloud data, the triangulated network model is established using the triangulation algorithm; Calculate the normal vector of the triangulated mesh based on the triangulated mesh model, and normalize the normal vector of the triangulated mesh to the unit sphere space to obtain the normalized result of the triangulated mesh normal vector; Sort all triangles in the triangulated network model to obtain the sorting result; Based on the normalization result of the triangulated network normal vector, the initial cluster center V is estimated, and the fuzzy clustering is iteratively completed to obtain the fuzzy clustering result; Based on the sorting results and fuzzy clustering results, the predicted growth objects are pre-screened and the regional growth seeds are replaced until the structural surface segmentation is completed and the separation results of all structural surfaces are obtained; Sort all triangles in the triangulated network model, including: Sort all triangles in the triangulated network based on the distance R from the triangle center to the origin. If multiple triangles are located in the same sphere, sort them by elevation. After the sorting is completed, adjacent triangles are within a spherical shell of a certain thickness, that is: sort(R)→R1≤R2…≤R n ; The pre-screening of the predicted growth objects specifically includes: When the growing seed is located within a small sphere (R d1 ), then the predicted growth object is within the large sphere (R d2 ) and the spherical shell area outside the small sphere; the thickness of the spherical shell is determined by the maximum triangle size d max It was decided that in order to ensure that all predicted growth objects are located in this area, 5 times the maximum triangle size is taken as the pre-screened spherical shell thickness R0; Right now: R0=5*d max ; R d2 =R d1 +R0。 2. The method for rapid and automatic identification of structural surfaces based on high-precision point cloud data according to claim 1, characterized in that: Before processing the pre-processed point cloud data, the method further includes: By arranging multiple stations, the measurement area is scanned with high precision from multiple angles to obtain high-precision point cloud data from multiple stations.

3. The method for rapid and automatic identification of structural surfaces based on high-precision point cloud data according to claim 2, characterized in that: Point cloud stitching and noise reduction are performed on the high-precision point cloud data of multiple sites to obtain pre-processed point cloud data.

4. The method for rapid and automatic identification of structural surfaces based on high-precision point cloud data according to claim 1, characterized in that: Based on the preset value of the structural surface recognition accuracy, the triangle size of the corresponding triangulated network model is set, and then the Delaunay triangulation algorithm is used to establish the triangulated network model. The N triangular facets of the model are stored in the form of triangle vertices and vertex indices; the triangle vertices are the coordinates (x, y, z) of the point cloud, which is the same as the number of points in the point cloud; the vertex index is (a i , b i , c i )The three vertices are arranged in a clockwise direction.

5. The method for rapid and automatic identification of structural surfaces based on high-precision point cloud data according to claim 4, characterized in that: The calculation of the normal vector of the triangulated network specifically includes: According to the triangle vertex and vertex index, the vertex index is traversed and calculated as i(a i , b i , c i )'s triangle's external normal vector F i , and normalize it to the unit sphere space; the calculation method is as follows:

6. The method for rapid and automatic identification of structural surfaces based on high-precision point cloud data according to claim 5, characterized in that: The process of estimating the initial cluster center V and iteratively completing the fuzzy clustering specifically includes: If the initial cluster center and the number of clusters K are set, and the cosine distance is used to calculate the dissimilarity of the spherical space data, then the dissimilarity d of the i-th triangle relative to the j-th cluster center is ij for: d ij 2 =1-(F i ·V j ) 2 , F i ·V j is the vector F i With V j The vector product of Calculate the membership function matrix U of fuzzy clustering. For any triangle face i, its membership degree u to the jth cluster center is ij for: If the number of clusters is not set, the traversal will start from 2; m is the fuzziness, m=2 is the default value of the program, and m can be changed according to the actual situation; If the initial cluster center and the number of clusters K are not set, a random algorithm will be used to generate the membership function matrix U, and then the cluster center V will be calculated; the calculation of the j-th cluster center is: Then calculate the membership function matrix U under this cluster center; The new cluster center V* is calculated by the membership function matrix U calculated above, and the new membership function matrix U* is calculated by the new cluster center V* until the objective function J of the fuzzy clustering is obtained. m When the (U, V) function is at its minimum, clustering is complete; the objective function J of fuzzy clustering is m The calculation of the (U,V) function is: When the objective function value J obtained in two adjacent iterations m With J m * When the difference is less than the set allowable error ε, the algorithm is judged to have converged, and the discriminant of the algorithm termination iteration is: J m -J m * <e, e=10 -5 。 7. The method for rapid and automatic identification of structural surfaces based on high-precision point cloud data according to claim 1, characterized in that: The step of replacing the regional growth seeds until the structural surface segmentation is completed specifically includes: I: Select a triangle as the growth seed; Ii: Search for a triangle in the spherical shell that shares a common edge with the seed triangle. This triangle is the triangle that may be needed for growth. III: Define the growth principle, and only perform region growing when the triangles with the same edge and the seed triangle have fuzzy clustering results; IV: Repeat steps i-iii above using the growing triangle as a seed triangle until the growth stops (no triangles with common edges that match the fuzzy clustering results are found in the spherical shell), completing the separation of a structural surface. V: Replace the new growth seed and repeat the above steps i-iv until all triangles are separated. At this time, all structural surfaces are separated.

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